product restructuring, exports, investment, and growth...

Product Restructuring, Exports, Investment, and

Growth Dynamics

(Job Market Paper)

Leilei Shen ∗

September 24, 2011

Abstract

This paper estimates a dynamic general equilibrium model of entry, exit, and endogenous pro-ductivity growth. Productivity is endogenous both at the industry level (firms enter and exit)and at the firm level (firms invest in productivity-enhancing activities). The focus of the paperis on two activities that make productivity-enhancing investments more attractive, namely, ex-porting and product-mix choices. A firm that increases its exports and/or its number of productswill have higher sales – and this makes investing in productivity more attractive because thereare more units (sales) across which the productivity gains can be applied. These insights aretaken to firm-level Spanish data. We compute the Markov Perfect Equilibrium using a nestedpseudo maximum likelihood estimator (NPL) with dynamic programming algorithms. Threekey findings emerge. First, there is no evidence of learning by exporting: the observed positivecorrelation between exporting and productivity operates entirely via the impact of exportingon productivity-enhancing investments. Restated, exporting decision raises productivity, butonly indirectly by making investing in productivity more attractive. Second, there is evidenceof learning by producing multiple products: product-mix raises productivity directly in additionto the investment channel. Third, there are strong complementarities among the product-mix,exporting and investment decisions. Finally, we simulate the effects of reductions in foreigntariffs. This increases exporting, investing, and wages; and wage increases decrease the numberof product produced per firm and force the least productive firms to exit. Productivity risesat the economy-wide level both because of the between firm reallocation effect and because ofwithin firm increases in productivity.

Keywords: heterogeneous firms, endogenous product range, dynamic discrete games, contin-uous games, multiple equilibria, pseudo maximum likelihood estimation, entry, exit, and growthin monopolistic competition

JEL Classifications: F12, F13, F14, L11, O31, O33.

∗PhD Candidate, Department of Economics, University of Toronto, 150 St. George Street, Toronto, OntarioM5S 3G7, Canada. Email: [email protected]. I would like to thank Daniel Trefler, Victor Aguirregabirial,Loren Brandt, John Sutton, and Peter Morrow, for their invaluable guidance and insightful conversations, and theparticipants of the University of Toronto Economics Seminar for helpful comments. All remaining errors are mine.

Product Restructuring, Exports, Investment, and Growth Dynamics Leilei Shen

Introduction

Gains from trade through both comparative advantage effects and intra-industry resource re-

allocations have been examined intensively in the past ( Melitz (2003) and Bernard et al. (2003)).

One element that is missing from this literature is the existence of multi-product firms that under-

take investments that lead to higher productivity, a higher propensity to export, and more products

produced. While multi-product firms that invest dominate international trade, comparatively little

research examines their production and export decisions and their productivity trajectory or how

these decisions are influenced by globalization.

A large empirical literature has emerged over the past decade trying to determine the causal

relationship between productivity and exporting. Much of it documents the self-selection of more

productive firms into the export market. The evidence that exporting raises productivity growth

rates is less uniform, with some studies (Clerides, Lach, and Tybout (1998), Bernard and Jensen

(1999), Bernard and Wagner (1997), Delgado, Farinas, and Ruano (2002) and Bernard and Jensen

(2004)) finding no such effect, and others finding varying degrees of support for a positive ef-

fect of exporting on productivity (Aw, Chung, and Roberts (2000),Baldwin and Gu (2003), Van

Biesebroeck (2004), Lileeva (2004), Hallward-Driemeier, Iarossi, and Sokoloff (2005), Fernandes

and Isgut (2006), Park et al. (2006), Aw, Roberts, and Winston (2007), De Loecker (2010) and

Lileeva and Trefler (2007)). Two theoretical papers, Atkeson and Burstein (2007) andConstantini

and Melitz (2008), have formalized how trade liberalizations can increase the rate of return to a

firm’s investment in new technology and thus lead to future endogenous productivity gains. Both

papers share several common features: first, productivity is the underlying state variable that dis-

tinguishes heterogeneous producers; second, productivity evolution is endogenous, affected by the

firm’s investment decisions; and third, they each identify pathways through which export market

size affects the firm’s choice to export or invest.

Very little research has focused on the combination of investment, exporting and multi-product

decision in a general equilibrium framework. This paper develops a tractable dynamic general equi-

librium model of endogenous product selection and productivity growth that offers a natural and

intuitive explanation for key features of the Spanish firm level data. Our model and empirical anal-

ysis demonstrate the importance of firm and industry endogenous productivity growth in response

− 1 −


to trade liberalization. In every period, firms make decisions about entry and exit, investment,

number of products, and exporting, and compete in a monopolistic competition product market.

Following Bernard, Redding, and Schott (forthcoming) which builds on Melitz (2003), we allow

firms to produce multiple products of varying profitability. We assume firm profitability in a par-

ticular product increases with two stochastic and independent draws in the first period the firm

operates. The first is firm productivity, which is drawn stochastically after the firm enters and

pays the sunk fixed entry cost. This governs the amount of labor that must be used to produce a

unit of output. Firm productivity becomes a state variable in all subsequent periods and evolves

over time based on firm investment and random shocks and/or depreciation. The second is firm-

product consumer tastes drawn every period, which regulate the demand for a firm in a market.

We assume both draws are revealed to firms after incurring a sunk cost of entry. If firms decide

to enter after having observed these draws, they face fixed and variable costs for each good they

choose to supply to a market as well as a fixed cost of serving each market that is independent

of the number of goods supplied. We assume consumers possess constant elasticity of substitution

preferences on the demand side as in Dixit and Stiglitz (1977). Demand for product variety de-

pends on the own-variety price, the price index for the product, and the price indices for all other

products. If a firm is active in a product market, it manufactures one of a continuum of varieties

and so is unable to influence the price index for the product. This implies the price of a firm’s

variety in one product market influences only the demand for its varieties in other product markets

through the price indices. Therefore, the firm’s inability to influence the price indices implies that

its profit maximization problem reduces to choosing the price of each product variety separately

to maximize the profits derived from that product variety. The structure of our model eliminates

strategic interaction within or between firms.

In this paper we develop an algorithm for computing the Markov Perfect Equilibrium (MPE)

similar to C. Lanier Benkard and Weintroub (2007a)1 and C. Lanier Benkard and Weintroub

(2007b). A nice feature of the algorithm is that, unlike existing methods, there is no need to place

a priori restrictions on the number of firms in the industry or the number of allowable states per

1C. Lanier Benkard and Weintroub (2008) define an oblivious equilibrium in which each firm is assumed to makedecisions based only on its own state and knowledge of the long-run average industry state, but where firms ignorecurrent information about competitors’ states. They showed that as the market becomes large, if the equilibriumdistribution of firm states obeys a certain “light-tail” condition, then the oblivious equilibrium closely approximatesMPE.

− 2 −


firm. These are determined by the algorithm as part of the equilibrium solution. In the past,

for Ericson and Pakes (1995) type models, MPE are usually computed using iterative dynamic

programming algorithms (e.g. Pakes and McGuire (1995)).However, computational requirements

grow exponentially with the number of firms and possible firm produtivity levels, making dynamic

programming infeasible in many problems of practical interest. In this paper, we take a different

tack and consider algorithms that can efficiently deal with any number of firms in a monopolistic

competition setting. This is most closely related to Hopenhayn (1992) and Melitz (2003). As in

Hopenhayn (1992), the analysis is restricted to stationary equilibria. Firms correctly anticipate this

stable aggregate environment when making all relevant decisions. This becomes computationally

feasible for MPE computation with common dynamic programming algorithms. We also use nested

pseudo likelihood (NPL), a recursive extension of the two-step pseudo maximum likelihood (PML),

that addresses inconsistent or very imprecise nonparametric estimates of choice probabilities to

compute the MPE.

The reason to model the investment, multi-product and exporting decisions jointly is they

are dependent on each other. Firms cannot export or produce multiple products, or have a lower

probability of doing so, below a certain productivity cut-off. Therefore firms need to invest and

increase their productivity in order to export and produce more products. The return to investment

is higher for exporting and multi-product firms, which makes the probability that the firm will

choose to invest dependent on the firm’s export status and the number of products produced. This

paper estimates a structural model of endogenous entry, exit, exports, product restructuring and

investment to evaluate the role that fixed costs of operating, sunk entry costs, cost of investment

and trade liberalization play in explaining the observed cross industry heterogeneity. Olley and

Pakes (1996) show that ignoring endogenous market exit can generate significant biases in the

estimation of production functions. The estimation of structural models of market entry is based

on the Principle of Revealed Preference. In the context of these models, this principle establishes

that if we observe a firm operating in a market it is because its value in that market is greater than

the value of shutting down and putting its assets to alternative uses. Under this principle, firms’

entry decisions reveal information about the firm’s underlying latent profit (or value). The same

for firms exit decisions.

Since our data do not provide firm-product-destination export information, we simplify the

− 3 −


demand parameter in Bernard, Redding, and Schott (forthcoming) to firm-product level only.

However, it is very simple to model the demand parameter in firm-product-destination level. The

main results of this paper should still hold with data that support this kind of model.

The model yields a rich set of predictions on productivity, investment, product restructuring

and exporting. First, firms self-select into exporting, investment, and range of products based

on their current productivity. Productivity evolves over time and is endogenous and positively

impacted by both investment and number of products produced. The direct positive impact on

productivity from the number of products produced suggests learning by doing. However, there

is no evidence of learning by exporting: the observed positive correlation between exporting and

productivity operates entirely via the impact of exporting on productivity-enhancing investments.

Past exporting is correlated with current productivity via past investing; that is, past exporting

complements past investing which leads to current productivity gains. Second, there are strong

complementarities among exporting, range of products and investment decisions. A rise in the

number of products raises productivity by making investment more attractive. (There is also a

direct impact of the number of products on productivity, which we conjecture captures unmeasured

investments in new products). Finally, we simulate the effects of reductions in foreign tariffs. This

increases exporting, investiment and wages; and wage increases cause a reduction in the number of

products per firm and force the least productive firms to exit. Productivity rises at the economy-

wide level both because of the between firm reallocation effect and because of within firm increases

in productivity

The rest of paper is organized as follows. In Section 1 we outline the dynamic industry model.

In Section 2 we define and solve for MPE. In Section 3 we discuss the data used and the limitations to

the data. In Section 4 we provide our main result, namely, the role that product differentiation, fixed

costs of operating, sunk entry costs, cost of investment and trade liberalization play in explaining

the observed cross industry heterogeneity. In Section 5 we discuss the counterfactuals. Finally,

Section 6 presents conclusions, policies and a discussion of future research directions. All proofs

and mathematical arguments are provided in the Appendix.

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1. The Model

Consider a world consisting of many countries and many products. Firms decide whether to pro-

duce, what products to make,and where to export these products. Products are imperfect substi-

tutes of each other, and within each product firms supply horizontally differentiated varieties. For

simplicity, we develop the model for symmetric products and n symmetric countries.

1.1. Static Model

1.1.1. Consumers

The world consists of a home country and a continuum of n foreign countries, each of which is

endowed with Ln units of labor that are supplied inelastically with zero disutility.

Consumers prefer more varieties to less and consume all differentiated varieties in a continuum

of products that we normalize to the interval [0,1]. The utility function of a representative consumer

in country j is given by:

U =

[∫ 1

0Cνjkdk

]1/ν

, 0 < υ < 1, (1)

as in the standard Dixit and Stiglitz (1977) form, where k indexes products. Within each product, a

continuum of firms produce horizontally differentiated varieties of the product. Cjk is a consumption

index for a representative consumer in country j for product k and is of the form:

Cjk =

[∫ n+1

0

∫ω∈Ωijk

[λjk (ω) cijk (ω)]ρ dωdi

]1/ρ

, 0 < ρ < 1, (2)

where i and j index countries, ω indexes varieties of product k supplied from country i to j

and Ωijk denotes the endogenous set of these varieties. Similar to Bernard, Redding, and Schott

(forthcoming) the demand shifter λjk (ω) captures the strength of the representative consumer’s

tastes for firm variety ω and reflects demand heterogeneity. λjk (ω) can also be interpreted as the

quality of variety ω. We assume σ ≡ 11−ρ > κ ≡ 1

1−ν or the elasticity of substitution across varieties

within products is greater than the elasticity of substitution across products and σ is the same for

− 5 −


all products. The corresponding price index for product k in country j is:

Pjk =

[∫ n±1

0

∫ω∈Ωijk

(pijk (ω)

λijk (ω)

)1−σdωdi

] 11−σ

. (3)

Furthermore, countries are also symmetric, and the only difference between the domestic market

and each export market is that a common value of trade costs has to be incurred for each export

market. Therefore, instead of indexing variables in terms of country of production, i, and market of

consumption, j, we distinguish between the domestic market, d, and each export market, x, except

where otherwise indicated.

1.1.2. Production

The only factor of production is labor as in Melitz (2003). The potential entrants are identical

prior to entry. A potential entrant who decides to stay out of the market gets zero profits. If

the firm decides to enter, it must incur a sunk entry cost fEN,i > 0 units of labor in country i.

fEN,i = fEN,i + εEN,it at time t, where fEN,i is the component of entry cost that is common to

all the firms in the market in country i, and εEN,it is a firm-specific component which is private

information to the firm, has zero mean, and is i.i.d. over firms and over time. Similar to Bernard,

Redding, and Schott (forthcoming) we augment the model to allow firms to manufacture multiple

products and to allow for demand heterogeneity across products. The new entrant is not active

until the next period. Furthermore, the initial quality and the product attributes that influence

demand (consumer tastes λ) of a new entrant are uncertain when the firm makes its entry decision,

and they are not realized until the next period. The initial productivity ϕ is common across all

of a firms’s products and is a random draw from the probability function g(ϕ) with cumulative

distribution function G(ϕ).Consumer tastes for a firm’s varieties, λk ∈ [0,∞), vary across products

k and are drawn separately for each product from the probability function z(λ) with cumulative

distribution function Z(λ). To make use of law of large number results, we make simplifying

assumptions that productivity and consumer tastes distributions are independent across firms and

products, respectively, and of one another.

Once the sunk entry cost has been incurred in period t− 1, the potential entrant enters at the

end of period t− 1 and becomes an incumbent in period t. An incumbent in period t observes its

− 6 −


sell-off value φt and makes exit and investment decisions. If the sell-off value (or the exit value)

φt exceeds the value of continuing in the industry, then the firm chooses to exit, in which case it

earns the sell-off value and then ceases operations permanently. If it decides to stay and invest,

it faces fixed costs of supplying each market, which are fX > 0 for foreign market and fD > 0

for domestic market. These market specific fixed costs capture among other things the costs of

building distribution networks. In addition, we assume that the incumbent must pay the fixed

costs of supplying each product to a market, which are fx > 0 for foreign market and fd > 0

for domestic market. These product and market-specific fixed costs capture the costs of market

research, advertising, and conforming to foreign regulatory standards for each product. As more

products are supplied to a market, total fixed costs rise, but average fixed costs fall. The firm can

invest to improve its productivity for next period. A detailed modelling of the investment decision

is given under the Investment subsection.

In addition to fixed costs, there is also a constant marginal cost for each product that depends

on firm productivity, such that qk(ϕ, λk)/ϕ units of labor are required to produce qk(ϕ, λk) units

of output of product k. Finally, we allow for variable costs of trade, such as transportation costs,

which take the standard iceberg cost form, where a fraction τ > 1 of a variety must be shipped

in order for one unit to arrive in a foreign country. We assume for simplicity that the fixed costs

of serving each market are incurred in terms of labor in the country of production, although it is

straightforward to instead consider the case where they are incurred in the market supplied.

1.1.3. Firm-Product Profitability

Demand for a product variety depends on the own-variety price, the price index for the product

and the price indices for all other products. If a firm is active in a product market, it manufactures

one of a continuum of varieties and so is unable to influence the price index for the product. At

the same time, the price of firm’s variety in one product market only influences the demand for

its varieties in other product markets through the price indices. Therefore, the firm’s inability to

influence the price indices implies that its profit maximization problem reduces to choosing the

price of each product variety separately to maximize the profits derived from that product variety.

This optimization problem yields the standard result that the equilibrium price of a product variety

− 7 −


is a constant mark-up over marginal cost:

pd(ϕ, λd) =1

ρϕ, px(ϕ, λx) = τ

1

ρϕ, (4)

where equilibrium prices in the export market are a constant multiple of those in the domestic

market due to the trade costs; λd varies across products and λx varies across products and export

markets. We choose wage in one country as the numeraire, which together with country symmetry

implies w = 1 for all countries.

Demand for a variety is:

qd(ϕ, λd) = Qkλσ−1d

[pd(ϕ, λd)

P

]−σ, qx(ϕ, λx) = Qkλ

σ−1x

[px(ϕ, λx)

P

]−σ. (5)

Substituting for the pricing rule equation (4), the equilibrium revenue in each domestic and export

market are respectively:

rd(ϕ, λd) = E(ρPϕλd)σ−1, rx(ϕ, λx) = τ1−σ

(λxλd

)σ−1

rd(ϕ, λd), (6)

where E denotes aggregate expenditure on a product and P denotes the price index for a product

(subscript product k is suppressed here). The equilibrium profits from a product in each domestic

and export market are therefore:

πd(ϕ, λd) =rd(ϕ, λd)

σ− θd, πx(ϕ, λx) =

rx(ϕ, λx)

σ− θx. (7)

Firm productivity and consumer tastes enter the equilibrium revenue and profit functions in the

same way, because prices are a constant mark-up over marginal costs and demand exhibits a

constant elasticity of substitution.

Relative revenue from two varieties of the same product within a given market depends solely

on relative productivity and consumer tastes:

r(ϕ′, λ′) =

(ϕ′

ϕ

)σ−1(λ′λ

)σ−1

r(ϕ, λ). (8)

− 8 −


Similarly, as countries are symmetric, equation (7) implies that the relative revenue derived from

two varieties of the same product with the same values of productivity and consumer tastes in the

export and domestic markets depends solely on variable trade costs: rx(ϕ, λ)/rd(ϕ, λ) = τ1−σ.

A firm with a given productivity ϕ and consumer taste draw λ decides whether or not to supply

a product to a market based on a comparison of revenue and fixed costs for the product. For each

firm productivity ϕ, there is a zero-profit cutoff for consumer tastes for the domestic market, λ∗d (ϕ),

such that a firm supplies the product domestically if it draws a value of λd equal to or greater than

λ∗d (ϕ). This value of λ∗d (ϕ) is defined by:

rd(ϕ, λ∗d (ϕ)) = σθd. (9)

Similarly for the export market, λ∗x (ϕ) is given by:

rx(ϕ, λ∗x (ϕ)) = σθx. (10)

We can write λ∗d (ϕ) and λ∗x (ϕ) as function of their lowest productivity supplier, λ∗j (ϕj) for

j ∈ d, x, respectively:

λ∗j (ϕ) =

(ϕ∗jϕ

)λ∗j(ϕ∗j)

j ∈ d, x (11)

where ϕ∗j for j ∈ d, x is the lowest productivity at which a firm supplies the domestic and

the export market, respectively. As a firm’s own productivity increases, its zero-profit cutoff for

consumer tastes falls because higher productivity ensures that sufficient revenue to cover product

fixed costs is generated at a lower value of consumer tastes. In contrast, an increase in the lowest

productivity at which a firm supplies the domestic market, ϕ∗j , or an increase in the zero-profit

consumer tastes cutoff for the lowest productivity supplier λ∗j

(ϕ∗j

), raises a firm’s own zero-profit

consumer tastes cutoff. The reason is that an increase in either ϕ∗j or λ∗j

(ϕ∗j

)enhances the

attractiveness of rival firms’ products, which intensifies product market competition, and hence

increases the value for consumer tastes at which sufficient revenue is generated to cover product

fixed costs. Given τσ−1(θx/θd) > 1, a firm is more likely to supply a product domestically than to

export the product.

− 9 −


1.1.4. Firm Profitability

Having examined equilibrium revenue and profits from each product, we now turn to the firm’s

equilibrium revenue and profits across the continuum of products as a whole. As consumer tastes

are independently distributed across the unit continuum of symmetric products, the law of large

numbers implies that the fraction of products supplied to the domestic market by a firm with

a given productivity ϕ equals the probability of drawing a consumer taste above λ∗d(ϕ), that is

[1 − Z(λ∗d (ϕ))]. As demand shocks are also independently and identically distributed across the

continuum of countries, the law of large numbers implies that the fraction of foreign countries to

which a given product is exported equals [1−Z(λ∗x (ϕ))]. A firm’s expected revenue across the unit

continuum of products equals its expected revenue for each product. Expected revenue for each

product is a function of firm productivity ϕ and equals the probability of drawing a consumer taste

above the cutoff times expected revenue conditional on supplying the product. Therefore total firm

revenue across the unit continuum of products in the domestic and export markets is:

rj(ϕ) =

∫ ∞λ∗j (ϕ)

rj(ϕ, λj)z(λj)dλj j ∈ d, x . (12)

total profits for domestic and export market is:

πj(ϕ) =

∫ ∞λ∗j (ϕ)

[rj(ϕ, λj)

σ− fj

]z(λj)dλj − Fj j ∈ d, x (13)

Total profit is:

π(ϕ) = πd(ϕ) + πx(ϕ). (14)

Equilibrium revenue from each product within the domestic market, rj(ϕ, λj), is increasing

in firm productivity and consumer tastes. Hence the lower a firm’s productivity, ϕ, the higher its

zero-profit consumer tastes cutoff, λ∗d (ϕ), and the lower its probability of drawing a consumer tastes

high enough for a product to be profitable. Therefore firms with lower productivities have lower

expected profits from individual products and supply a smaller fraction of products to the domestic

market, [1−Z(λ∗d (ϕ))]. For sufficiently low firm productivity, the excess of domestic market revenue

− 10 −


over product fixed costs in the small range of profitable products falls short of the fixed cost of

supplying the domestic market, Fd. The same is true for export market.

The profit function satisfies the following properties:

1. Total profit for domestic and export market is increasing in ϕ.

2. For all ϕ ∈ R+ and t, π(ϕ) > 0 and supϕπ(ϕ) <∞.

3. lnπ(ϕ) is continuously differentiable.

4. Strengthened competition cannot result in increased profit due to competition for labor.

The increased labor demand by the more productive firms and new entrants bids up the real wages

and forces the least productive firms to exit. Work by Bernard and Jensen (1999) suggests that this

channel substantially contributes to U.S. productivity increases within manufacturing industries.

1.1.5. Aggregation and Market Clearing

An equilibrium will be characterized by a mass M of firms and a distribution g(ϕ) of productivity

levels over a subset of [0,∞). The weighted average productivity in the domestic and export market,

respectively, is:

ϕj =

[∫ ∞0

(ϕλj(ϕ)

)σ−1g(ϕ)dϕ

] 1σ−1

, j ∈ d, x , (15)

where λd(ϕ) denotes weighted-average consumer tastes in the domestic market for a firm with

productivity ϕ:

λj(ϕ) =

[∫ ∞0

(λj(ϕ))σ−1 z(λj)dλj

] 1σ−1

j ∈ d, x . (16)

The aggregate price index P is then given by:

P =

[Md

∫ ∞0

pd (ϕ)1−σ g(ϕ)dϕ+ nMx

∫ ∞0

px (ϕ)1−σ g(ϕ)dϕ

] 11−σ

=

[Md

(1

ρϕd

)1−σ+ nMx

(1

ρϕx

)1−σ] 1

1−σ

. (17)

The weighted average productivity of all firms (domestic and foreign) competing in a single

− 11 −


country is:

ϕ =

1

M

[Mdϕ

1−σd + nMx

(τ−1ϕx

)1−σ] 11−σ

. (18)

where the productivity of exporters is adjusted by the trade cost τ. Thus the aggregate price index

P and revenue R can be written as functions of only the productivity average ϕ and M :

P = M1

1−σ1

ρϕR = Mrd(ϕ). (19)

1.2. Dynamic Model

In this section we formulate the static model discussed in the previous section into a dynamic model.

The model evolves over discrete time periods and an infinite horizon. We index time periods with

non-negative integers t ∈ N (N = 0, 1, 2, ...) .

Firm heterogeneity is reflected through firm states. We refer to a firm’s state as its productivity

level. At time t, the productivity level of firm i is ϕit ∈ R+.We define the industry state st to be

the number of incumbent firms Mt and the average productivity ϕt in period t. We define the state

space S = s ∈ R2+|M ∗ ϕ <∞In each period, each incumbent firm earns profits. As in the static

model, a firm’s single period profit πt(ϕt, st) depends on its productivity ϕt and the aggregate price

index Pt, which can be written as a function of the productivity average ϕt and mass of firms Mt

in period t.

The model also allows for entry and exit. In each period, each incumbent firm observes a

positive real-valued sell-off value φit that is private information to the firm. If the sell-off value

exceeds the value of continuing in the industry, then the firm may choose to exit, in which case it

earns the sell-off value and then ceases operations permanently.

In each period potential entrants can enter the industry by paying a fixed entry cost fEN .

Entrants do not earn profits in the period that they enter. They appear in the following period

with productivity and consumer tastes drawn from g(ϕ) and z(λ) and can earn profits thereafter.

Each firm aims to maximize expected net present value. The interest rate is assumed to be positive

and constant over time, resulting in a constant discount factor of β ∈ (0, 1) per time period.

In each period, events occur in the following order:

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1. Each incumbent firm observes its sell-off value φit, productivity at t+1, and demand shocks.

2. The number of entering firms is determined and each entrant pays an entry cost of fEN .

3. Incumbent firms choose price and quantity to maximize profit.

4. Incumbent firms choose investment, exporting, and number of products to maximize the

expected net present values.

4. Exiting firms exit and receive their sell-off values.

5. Productivity in t+ 1 is realized and new entrants enter.

We assume that there are an asymptotically large number of potential entrants who play

a symmetric mixed entry strategy. This results in a Poisson-distributed number of entrants (see

Weintraub, Benkard, and Van Roy (2008b) for a derivation of this result). Our associated modeling

assumptions are as follows:

Assumption:

1. The number of firms entering during period t is a Poisson random variable that is

conditionally independent of ϕit, λit,εit|t > 0, conditioned on st.

2. fEN < βφ, where φ is the expected net present value of entering the market, investing

zero and earning zero profits each period, and then exiting at an optimal stopping time.

We denote the expected number of firms entering in period t, by MEN,t. This state-dependent

entry rate will be endogenously determined, and our solution concept will require that it satisfies a

zero expected discounted profits condition. Modeling the number of entrants as a Poisson random

variable has the advantage that it leads to simpler dynamics. However, other entry processes can

be used as well. Assumption 2 ensures that the sell-off value by itself is not sufficient reason to

enter the industry.

1.2.1. Evolution of Productivity

In order to model the firm’s dynamic optimization problem for exporting, investment, and product

restructuring decisions we begin with a description of the evolution of the process for firm produc-

tivity ϕit. We assume that productivity evolves over time as a Markov process that depends on

firm’s investment, its participation in the export market, the number of products firm produces,

− 13 −


and a random shock:

ϕit = z(ϕit−1, Iit−1, Xit−1,Nit−1) + ξit (20)

Iit−1, Xit−1, Nit−1 are, respectively, the firm’s investment, export market participation, and num-

ber of products produced in the previous period. Note that this specification is very general as

the function z may take on either positive or negative values (e.g., allowing for positive depreci-

ation).The inclusion of Iit−1 recognizes that the firm may affect the evolution of its productivity

by investing. The inclusion of Xit−1 allows for the possibility of learning-by-exporting, that par-

ticipation in the export market is a source of knowledge and expertise that can improve future

productivity. The inclusion of Nit−1 allows for the possibility of learning-by-doing, that producing

more products exposes the firm to a bigger pool of knowledge that can improve its future produc-

tivity. In the empirical section, we assess the strength of each of these decisions. The stochastic

nature of productivity improvement is captured by ξit which is treated as an iid shock with zero

mean and variance σ2ξ . This stochastic component represents the role that randomness plays in the

evolution of a firm’s productivity. Uncertainty may arise, for example, due to the risk associated

with a research and development endeavor or a marketing campaign.

We also assume there exists a positive constant z ∈ R+ s.t. |z(I,X,N, ε)| ≤ z, for all

(I,X,N, ε).There exists a positive constant I, X, N s.t. Iit < I, Xit < X, Nit < N, for all

i, t. This assumption places a finite bound on how much progress can be made or lost in a single

period. Under perfect capital market, firms cannot invest more than their expected net present

value2. Xit is modeled as a discrete 0/1 variable in the empirical section. If modelled as a contin-

uous variable, export volume is bounded by the consumer demand. Similarly, Nit is also bounded

by the consumer demand.

1.2.2. Dynamic Decisions- Investment, Exporting, and Product Restructuring

In this section, we develop the firm’s dynamic decision to export, invest and the number of products

to produce. If the firm instead decides to remain in the industry, then it must choose the number

2We assume perfect capital market, firms investment decisions are constrained by the net present value of thefirm, i.e. firms cannot borrow an infinite amount to increase their productivity. The role of imperfect capital marketis left for future research.

− 14 −


of products to produce, whether to export, and how much to invest to improve its productivity

level. We denote the unit cost of investment by d. We assume that the firm decides whether to

stay in operation after observing the scrap value φit, and make the number of products and export

decisions in year t after observing the fixed costs of operating in domestic market (Fd), export

market (Fx),and fixed costs for each additional product produced in domestic and export market,

(fd, fx) if it decides to remain in operation. We model these fixed costs as iid draws from a known

join distribution Gf . The firm i′s value function in year t if it chooses to continue, can be written

as:

V stay(ϕit, st) = maxXit

∫V Dλd

(ϕit, st)dGf ,

∫V Eλd

(ϕit, st)dGf

(21)

where Xit is a discrete 0/1 variable identifying the firm’s export choice in period t, V Dλd

(ϕit, st) is

the current and expected future profit from producing products in domestic market only:

V Dλd

(ϕit, st) = maxλ∗d

∫ ∞λ∗d

[rd(ϕ, λd)

σ− fd

]z(λd)dλd − Fd + V D(ϕit, st)

where V D(ϕit, st) is the value of a non-exporting firm after it makes its optimal investment decision:

V D(ϕit, st) =

∫ maxIit

βEtVit+1(ϕit, st+1|Xit = 0, Nit = [1− Z(λ∗d)] , Iit = Iit)

−dIit − 1(Iit>0)fI

dGf

where if firm chooses to invest Iit, it incurs the cost of investment dIit and a fixed cost compo-

nent of investment fI . It has an expected future return which depends on how investment affects

future productivity. Similarly V Eλd

(ϕit, st) is the current and expected future profit from producing

products in both domestic and export market:

V Xλd

(ϕit, st) = maxλ∗d

∫ ∞λ∗d

[rd(ϕ, λd)

σ− fd

]z(λd)dλd − Fd

+ maxλ∗x

∫ ∞λ∗x

[rx(ϕ, λx)

σ− fx

]z(λx)dλx − Fx + V E(ϕit, st)

− 15 −


where V E(ϕit, st) is the value of an exporting firm after it makes its optimal investment decision:

V X(ϕit, st) =

∫ maxIit

βEtVit+1(ϕit, st+1|Xit = 1, Nit = [1− Z(λ∗d)] , Iit = Iit)

−dIit − 1(Iit>0)fI

dGf

This shows that the firm chooses to export in year t when the current plus expected gain in

future export profit exceeds the relevant fixed cost of exporting. Finally, to be specific, the expected

future value conditional on different choices for Xit, Nit,and Iit for firm staying in operation is:

EtVstay(ϕit+1, st+1|Xit,Nit, Iit) =

∫s′

∫ϕ′

V stay(ϕ′, s′)dF (ϕ′|Xit,Nit, Iit)dP (s′|st).

In this equation the evolution of productivity dF (ϕ′|Xit,Nit, Iit) is conditional on Xit,Nit, and

Iit because of the assumption in equation (21). In this framework, the net benefit of product

restructuring, exporting and investment are increasing in current productivity. This leads to the

usual selection effect where high productivity firms are more likely to produce more products,

export, and invest. By making future productivity endogenous this model recognizes that current

choices lead to improvements in future productivity and thus more firms will self-select into, or

remain in, multi-products, exporting and investment in the future.

After observing φit, if the firm chooses to exit, its exiting value function is current period profit

with optimized Xit(ϕit, st), Nit(ϕit, st), Iit(ϕit, st) decisions plus the scrap value of exit:

V exit(ϕit, st) =

∫[π(ϕit, st, Nit(ϕit, st), Xit(ϕit, st), Iit(ϕit, st))] + φitdG

f

where

maxIit

βπ(ϕit, st, Nit(ϕit, st), Xit(ϕit, st), Iit(ϕit, st)) =

πd(ϕit, st, Nit(ϕit, st)) + 1(Xit(ϕit,st)=1)πx(ϕit, st, Nit(ϕit, st))− dIit(ϕit, st)− 1(Iit(ϕit,st)>0)fI

Firm i stays in operation in period t if V stay(ϕit, st) > V exit(ϕit, st).

− 16 −


2. Equilibrium

As a model of industry behavior we focus on pure strategy Markov perfect equilibrium (MPE), in

the sense of Maskin and Tirole (1988). We further assume that equilibrium is symmetric, such that

all firms use a common stationary investment, export, product restructuring and exit strategy. In

particular, there is a function I,X,N such that at each time t, each incumbent firm i invests an

amount Iit = I(ϕit, st), exports amount Xit = X(ϕit, st), and produce Nit = N(ϕit, st) number of

products. Similarly, each firm follows an exit strategy that takes the form of a cutoff rule: there is

a real-valued function η such that an incumbent firm i exits at time t if and only if φit ≥ η(ϕit, st).

Weintraub, Benkard, and Van Roy (2008b) show that there always exists an optimal exit strategy

of this form even among very general classes of exit strategies. Let Γ denote the set of investment,

export, product restructuring and exit strategies such that an element µ ∈ Γ is a set of functions

µ = (I,X,N, η), where I : R+ x S− > R+ is an investment strategy, X : R+ x S− > R>0 is an

export strategy, N : R+ x S− > N is a number of products to produce strategy, and η : R+ x

S− > R+ is an exit strategy. Similarly we denote the set of entry rate functions by Ω, where an

element of Ω is a function $ : S− > R+.

We define the value function V (ϕ|µ,$) to be the expected net present value for a firm at state

(productivity) ϕ when its competitors’ state is s,given that its competitors each follows a common

strategy µ ∈ Γ, the entry rate function is $ ∈ Ω, and the firm itself follows strategy µ ∈ Γ. In

particular,

V (ϕ, s|µ,$) = Eµ,$

[Ti∑k=t

βk−t (π(ϕik, sk, µ (ϕik, sk))) + βTi−tφi,Ti |ϕit = ϕ, st = s

], (22)

where Ti is a random variable representing the time at which firm i exits the industry, and the

subscripts of the expectation indicate the strategy followed by firm i and its competitors, and the

entry rate function.

An equilibrium to our model consists of an investment, export, product restructuring, and

exit strategy µ = (I,X,N, η) ∈ Γ,and an entry rate function $ ∈ Ω that satisfy the following

conditions:

− 17 −


1. Incumbent firm strategies represent a MPE:

supµ′V (ϕ, s|µ′, µ,$) = V (ϕ, s|µ,$) ∀ϕ ∈ R+, ∀s ∈ S. (23)

2. At each state, either the entrants have zero expected discounted profits or the entry

rate is zero (or both):

∑s∈S $(s) (βEµ [V (ϕ, st+1|µ,$)|st = s]− fEN ) = 0

βEµ,$ [V (ϕ, st+1|µ,$)|st = s]− fEN ≤ 0 ∀s ∈ S

$(s) ≥ 0 ∀s ∈ S.

And the labor market clears in each period. Weintraub, Benkard, and Van Roy (2008b) showed

that the supremum in part 1 of the definition above can always be attained simultaneously for all

ϕ and s by a common strategy µ′.

Doraszelski and Satterthwaite (2007) establish existence of an equilibrium in pure strategies

for a closely related model. We do not provide an existence proof here because it is long and

cumbersome and would replicate this previous work. With respect to uniqueness, in general we

presume that our model may have multiple equilibria.3

Dynamic programming algorithms can be used to optimize firm strategies and equilibria to

our model can be computed via their iterative application without the curse of dimensionality

problem commonly seen in the IO literature because st can be completely characterized by ϕt.

Stationary points of such iterations are MPE. An algorithm for computing the MPE is included

under Empirical Analysis section.

2.0.3. Market Clearing:

The feasibility constraint on the investment and entry is: MEN,tfEN = LEN,t, Mt(dIt) = LI,t.Total

payments to labor used in entry are equal to expected discounted profits LEN,t = Mtvt, where

vt =∫V (ϕ, st)Mt(st)g(ϕ)dϕ. The evolution of the distribution of operating firms Mt over time

is given by the optimal strategy µ consisting of I,X,N, η and entry rate $. Total payments to

labor used in production and investment, on the other hand, are equal to revenue minus expected

3Doraszelski and Satterthwaite (2007) also provide an example of multiple equilibria in their closely related model.

− 18 −


discounted profits, Lp,t+LI,t = R−Mtvt Combining these two expressions, L = R. Thus the labor

market clears: LEN,t + LI,t + Lp,t = L.

3. Empirical Analysis

We begin with a description of the evolution of the process for firm productivity ϕit. We assume

that productivity in period t evolves over time as a Markov process that depends on the firm’s

investments Iit−1 in period t-1, its participation in the export market Xit−1 in period t-1, the

number of products firm produces Nit−1 in t− 1 and a random shock:

lnϕit = α0 + α1 lnϕit−1 + α2 lnϕ2it−1 + α3 lnϕ3

it−1

+α4 ln Iit−1 + α5Xit−1 + α6Nit−1 + ξit. (24)

Here we model investment as a continuous choice to allow for the possibility that firms can increase

their productivity faster by investing more. The inclusion of Xit−1 recognizes that the firm may

affect the evolution of its productivity through learning-by-exporting. The inclusion of Nit−1 allows

the possibility of expanding into multiple products to have an effect on productivity. The stochastic

nature of productivity improvement is captured by ξit which is treated as an iid shock with zero

mean and variance σ2ξ . This stochastic component represents the role that randomness plays in the

evolution of a firm’s productivity. This is the change in the productivity process betweent−1 and t

that is not anticipated by the firm and by construction is not correlated with ϕit−1, Iit−1, Xit−1,and

Nit−1.This allows the stochastic shocks in period t to be carried forward into productivity in future

years.

3.1. Algorithm

To compute the MPE with the two-step-PML method, the beliefs about transition, entry, invest-

ment, export and exit strategies are computed non-parametrically. The second step is to construct

a likelihood function using those beliefs and estimate the structural parameters of interest. When

consistent nonparametric estimates of choice probabilities either are not available or are very im-

precise, we can use k-step-PML or NPL algorithm to compute the MPE. NPL works as follows,

start with any set of beliefs/strategies and compute the structural parameters of interest, update

− 19 −


strategies with the estimated structural parameters non-parametrically, then construct likelihood

function and update the structural parameters. Repeat this k times until the strategies converge.

3.1.1. Demand and Cost Parameters

We begin by estimating the domestic demand, marginal cost and productivity evolution pararme-

ters. The domestic revenue function for a single product firm in log form with an iid error term uit

that reflects measurement error in revenue or optimization errors in price choice is:

ln rd,it = (σd − 1) ln

(σd − 1

σd

)+ (σd − 1) lnϕit

+ lnEt + (σd − 1) lnPt + (σd − 1)λit + uit (25)

where λit is the unobserved demand shock for firm i in domestic market in time t. The composite

error term (σ − 1) ln (ϕit) + uit contains firm productivity. Since the inputs are observed at firm

level, using the product-level information requires an extra step of aggregating the data at the

product level to the firm level. From equation (25) I can aggregate the production function to the

firm level by assuming identical production functions across products produced which is a standard

assumption in empirical work, see for instanceBernard and Jensen (2008) and De Loecker (2010).

Under this assumption, and given that I observe the number of products each firm produces, I can

relate the average production of a given product k of firm Qikt to its total input use and the number

of products produced. The production function for product k of firm i is then given by:

Qikt = N−1it Qit (26)

where N is the number of products produced. Introducing multi-product firms in this framework

explicitly requires to control for the number of products product. Combining the production

function and the expression for price from equation (4) leads to an expression for total revenue

as a function of inputs, productivity, and the number of products.

ln rd,it = lnNit + (σd − 1) ln

(σd − 1

σd

)+ (σd − 1) lnϕit

+ lnEt + (σd − 1) lnPt + (σd − 1) lnλit + uit (27)

− 20 −


where λit is the average unobserved demand shock across all products for firm i in time t and N

is the number of products produced. For a single product firm, ln(1) = 0, and therefore this extra

term cancels out, whereas for multi-product firms an additional term is introduced.

We estimate firm productivity using Olley and Pakes (1996) and Levinsohn and Petrin (2003)

approach to rewrite the unobserved productivity in terms of expenditure on intermediate goods

for each firm. In general, the firm’s choice of the variable input levels for materials, mit, and

electricity, eit, will depend on the level of productivity and the demand shocks (which are both

observable to the firm). Under our model setting, marginal cost is constant in output, the relative

expenditures on all the variable inputs will not be a function of total output and thus not depend

on the demand shocks. In addition, differences in productivity will lead to variation across firms

and time in the mix of variable inputs used. Thus, material and energy expenditures by the firm

will contain information on productivity level. We can write the level of productivity, conditional

on the number of products produced, as a function of the variable input levels:

ϕit = ϕit(Nit,mit, eit) (28)

We can rewrite (27) as follows:

ln rd,it = γ0 +T∑t=1

M∑m=1

γmtDmDt + h(Nit,mit, eit) + vit (29)

where intercept γ0 is the demand elasticity terms, Dt is the time varying aggregate demand shock,

Dm is the market-level factor prices,mit is expenditure on intermediate goods, and h(.) captures

the effect of productivity on domestic revenue. We specify h(.) as a cubic function of its arguments

and estimate (28) with OLS. The fitted value of the h (.) function, which we denote hit is an

estimate of lnNit+ (σ − 1) lnϕit. Next, we can construct an estimate of productivity for each firm.

Substituting lnϕit = (h− lnNit)/ (σ − 1) into productivity evolution equation (24):

hit − lnNit = α∗0 + α1(hit−1 − lnNit−1) + α2(hit−1 − lnNit−1)2 + α3(hit−1 − lnNit−1)3

+α∗4 ln Iit−1 + α∗5Xit−1 + α∗6Nit−1 + ξ∗it. (30)

where the star represents that the α coefficients are multiplied by (σd − 1) . This equation can be

− 21 −


estimated with nonlinear least squares and the underlying parameters α can be retrieved with an

estimate of demand elasticities σd. We can estimate the demand elasticities using data on total

variable cost. Total variable cost is an elasticity-weighted combination of total revenue in each

market:

tvcit = ρd ∗ rd,it + ρx ∗ rx,it + εit (31)

where ρj = 1 − 1/σj for j = d, x. Finally given estimate of σd, we can construct an estimate of

productivity for each observation as:

ln ϕit = (h− lnNit)/ (σd − 1) . (32)

Three aspects of this static empirical model are worth mentioning. First, because firm hetero-

geneity plays a crucial role in both the domestic and export market, we utilize data on firm revenue

to estimate firm productivity. Second, we’ve also used total variable costs to estimate demand

elasticities in both export and domestic market. Third, estimation of the process for productivity

evolution is important for firm’s dynamic investment equations because the parameters from equa-

tion (30) are used directly to construct the value functions that underlie firm’s investment, export,

and number of products choice.

The Melitz (2003) framework assumes the only factor of production is labor. For a Cobb-

Douglas technology, the domestic revenue function becomes:

ln rd,it = lnNit + (σd − 1) ln

(σd − 1

σd

)+ (σd − 1) (β0 − βk ln kit − βω lnωt + lnϕit)

+ lnEt + (σd − 1) lnPt + (σd − 1) lnλit + uit (33)

where kit is firm’s capital stock and ωt is a vector of variable input prices common to all firms.

Productivity, conditional on the number of products produced and capital stock, can be written as

a function of the variable input levels: ϕit = ϕit(Nit,mit, eit). Equation (29) becomes :

ln rd,it = γ0 +

T∑t=1

M∑m=1

γmtDmDt + h(Nit, kit,mit, eit) + vit (34)

− 22 −


The fitted value of the h(.) function, denoted hit, is an estimate of lnNit+(σ − 1) (−βk ln kit+lnϕit).

Next, we can construct an estimate of productivity for each firm by substituting lnϕit = (h −

lnNit)/ (σ − 1) + βk ln kit into productivity evolution equation (24). The productivity evolution

equation can be estimated with nonlinear least squares and the underlying βk parameter can be

retrieved given an estimate of σd. Finally, given estimates of βk and σd, we can construct an

estimate of productivity for each firm as:

ln ϕit = (h− lnNit)/ (σd − 1) + βk ln kit. (35)

3.1.2. Dynamic Parameters

The algorithm below is designed to compute the beliefs about transition, entry, investment, export,

exit strategies and the value function associated with these strategies with a positive entry rate

given some values of structural parameters. It starts with two extreme entry rates: $ = 0 and

$ =1

fEN

(supϕ,s π(ϕ, s)

1− β+ φ

). Any equilibrium entry rate must lie in between these two extremes.

The algorithm searches over entry rates between these two extremes for one that leads to the

MPE strategies and the value function associated with these strategies given a set of structural

parameters. For each candidate entry rate, an inner loop (step6-10) computes an MPE firm strategy

for that fixed entry rate. Strategies are updated smoothly (step 9).4 If the termination condition

is satisfied with ε1 = ε2 = 0, we have a set of MPE beliefs given structural parameters.

The algorithm is easy to program and computationally efficient. In each iteration of the inner

loop, the optimization problem to be solved is a one dimensional dynamic program. The state space

in this dynamic program is the set of productivity levels a firm can achieve. In principle, there

could be an infinite number of them. However, beyond a certain productivity level the optimal

strategy for a firm is not to invest, so its quality cannot increase to beyond that level.

4The parameters γand N were set after some experimentation to speed up convergence.

− 23 −


4. Data

4.1. Spanish Firm Level Data

The model developed in the last section will be used to analyze the sources of productivity change

of firms in Spain. The micro data used in estimation was collected by SEPI Foundation in Spain for

the years 1999-2008. The products are classified into 20 manufacturing industries based on 3-figure

CNAE-93 codes.

The data set we use is a collection of 3216 firms that operated in at least one of the five years

between 1999–2008 and that reported necessary data on domestic and export revenue, investment,

total variable costs, and number of products they are producing. Only 848 of those firms operated

in all tenS years between 1999-2008.

Table 1 provides the summary measures of the size of the firms, measured in revenues and

average employment. The top panel of the table provides the median firm size across operating

firms in our sample in each year, while the bottom panel summarizes the average firm size. The

first column shows that approximately 35 percent of the firms that do not export in a given year.

The median firm’s domestic revenue varies from 14.34 to 17.46 in hundred of thousands of Euros.

Among the exporting firms, the median firm’s domestic revenue is approximately eight times as

large, 10.5 to 12.9 million Euros. The export revenue of the median firm ranges from 3.4 to 5.5

million Euros. The median number of products for both exporters and non-exporters are 1, while

the average number of products produced by non-exporters ranges from 1.07 to 1.14 and the 1.13

to 1.15 for exporters.

The distribution of the firm revenue is highly skewed, particularly for firms that participate in

the export market. The average domestic firm revenues are larger than the medians by a factor of

approximately six for the exporting firms and the average export revenues are larger by a factor of

approximately 10. The skewness in the revenue distributions can also be seen from the fact that

the 100 largest firms in our sample in each year account for approximately 40 percent of the total

domestic revenue and 75 percent of the export revenue. The skewness in revenues will lead to large

differences in profits across firms and a heavy tail in the profit distribution. To fit the participation

patterns of all the firms it is necessary to allow the possibility that a firm has large fixed and/or

− 24 −


sunk costs. We allow for this in our empirical model by assuming exponential distributions for the

fixed and sunk costs. Together this assumption allows for substantial heterogeneity in the costs

across plants.

The other important variable in the data is the number of products the firms choose to produce.

Number of products in the sample is defined as the number of products at 3 figures CNAE-93 each

firm produces. Even though in the sample only five percent of the firms produce more than 1

product, they account for 20 percent of the total domestic revenue and 25 percent of the export

revenue.

The last important variable in the data is the investment the firms make each year. Table 2

provides summary statistics for different measures of investment for exporters and non-exporters.

We look at two measures of investment. The first one is investment on capital goods which includes

the purchases of information processing equipment, technical facilities, machinery and tools, rolling

stock and furniture, office equipment and other tangible fixed assets. The second one is total

expenses on R&D which is the sum of the salaries of R&D personnel (researchers and scientists),

material purchases for R&D, and R&D capital (equipment and buildings) expenses. The first

column in Table 2 provides the percentage of firms with positive investment in capital in each year.

In our sample, approximately 70 percent of the non-exporters invest in capital where close to 90

percent of the exporters invest in capital. Only 10 percent of non-exporters induce R&D expenses,

whereas 50 percent of the exporters induce R&D expenses. The top panel of the second column

provides the median of the capital investment given positive investment from operating firms, and

the bottom panel provides the mean of the capital investment given positive investment. The

average positive investment in capital is approximately ten times as large as the median positive

capital investment for non-exporters and six times for exporters. All numbers in the table are

expressed in tens of thousands of Euros. Median investment in capital for non-exporters ranges

from 40 to 50 thousand Euros and 500-700 thousand Euros for exporters. Average investment in

capital for exporters is approximately seven times that of the non-exporters. The average positive

R&D expenses are approximately 5 times the median positive R&D expenses for non-exporters,

and ten times of that for exporters. The difference in mean and median of the R&D expenses

between non-exporters and exporters is also approximately ten folds.

− 25 −


4.2. Empirical Transition Patterns for Entry/Exit, Investment, and Export

In this section we summarize the patterns of entry, exit, R&D and exporting behavior in the sample,

with a focus on the transition patterns that are important to estimating the fixed and sunk costs

of entry, R&D, and exporting. Table 3 reports entry and exit rates over the years for firms that

operated at least one year during 1999-2008. Operating firms are defined as firms with positive

revenue. The first column reports the number of firms with positive revenue in each year. The

second column reports the number of non-operating firms in the sample. Column 3 and 4 report

the number of new entrants and exits in each year. New entrants are defined as firms generated

positive revenue in time period t and zero revenue in time period t-1. Similarly for exits, firms that

generated revenue in period t-1 but stopped operating in period t are defined as exits. In the year

2003, there are no new entrants and a high exit rate of 19 percent. This is the year following the

technology bubble and 911 . Year 2004 has no entry and close to zero exits. In the year 2005, entry

rate shot up to 33 percent with 7 percent of exit rate and in the year 2006 entry rate falls back to

15% and exit rate goes up to 10%. The average entry and exit rate for this time period is 14 and 9

percent. With significant entry and exit behaviors present, ignoring firms self selection into entry

and exit will result in biased estimates of investment and export decisions.

Table 4 reports the proportion of firms that undertake each combination of the activities and

the transition rates between pairs of activities over time. The top panel of Table 4 reports the

average proportion of operating firms in both period t and t+1 that undertake neither investment

nor export, investment only, export only, and both investment and export and the transition rates

between pairs of activities over time. The middle panel reports those for new entrants in period t

that continue to operate in t+1. The bottom panel reports those for firms that cease to produce

in t+2, but operate in both t+1 and t. The first row of each panel reports the cross-sectional

distribution of exporting and investment averaged over all years. It shows that in each year, the

proportion of operating firms undertaking neither of these activities is .11. This number is higher

for new entrants and firms that will cease to produce. The proportion that invest but do not export

is .25 for operating firms. This number is higher for new entrants and lower for firms that will cease

production in the sample, suggesting that new entrants are more likely to invest to improve their

productivity due to a bad luck in the productivity draw and firms that have a higher probability of

− 26 −


exit are the ones with lower productivity and therefore don’t bother to invest. The proportion that

export only and do not invest .07 for operating firms, .08 for new entrants and .11 for firms that

will exit. The proportion that do both for operating firms is .57, which is higher than the number

for new entrants and firms that will exit. Overall, 82% of the operating firms engage in investments

and 64% of the operating firms export5. One explanation for difference in export and investment

participation is that differences in productivity and the export demand shocks affect the return of

each activity and the firms self-select into each activity based on the underlying profits.

The transition patterns among investment and exporting are important for the model estima-

tion. The last four rows in each panel of the table report the transition rate from each activity in

year t to each activity in year t+1. Several patterns are clear. First, there is significant persistence

in the status over time for all three panels. This can reflect a high degree of persistence in the

underlying sources of profit heterogeneity, which in our model, is productivity and the export mar-

ket shocks. Of the operating firms that did neither activity in year t, .67 of them are in the same

category in year t+1. This number is .88 for firms that will exit and only .49 for new entrants.

This suggests that even though there is persistence in the status over time, different kind of firms

will have different level of persistence. New entrants that did not invest nor export are more likely

to invest than the incumbent firms and firms that will exit soon will be less likely to invest than

the incumbent firms. The probability of remaining in the same category over adjacent years is .79,

.49, and .92 for invest only, export only, and both for operating firms. These numbers are similar

for new entrants and firms that will soon exit except for invest only. Firms that will soon exit with

positive investment in period t are less likely to invest in t+1 when they decide to exit at the end

of period t+1. This differences in persistence reflect the importance of modeling firms self-selection

into entry and exit.

Second, firms that undertake one of the activities in year t are more likely to start the other

activity than a firm that does neither. This is true for all firms. If the firm does neither activity in

year t, it has a probability of .03 to enter the export market and .31 to invest in the next period for

operating firms. These number are .07 and .85 for firms that only invest in period t, .93 and .47 for

firms that only export in period t, and .98 and .94 for firms that do both in period t. Third, firms

5The export participation rate in Spain is comparable to those firms in France. The export participation rate ofFrench firms (with 20 employees or above) is 69.4% in 1990 and 74.8% in 2004.

− 27 −


that conduct both activities in year t are less likely to abandon one of the activities than firms that

only conduct one of them. Operating firms that conduct both activities have a .06 probability of

abandoning investment and a .02 probability of leaving the export market. Operating firms that

only do investment have a .15 probability of stopping in investment while firms that only export

have a .07 probability of stopping in export. Exiting firms that only do investment have a .44

probability of stopping and those who only do export have a .03 probability of stopping. Fourth,

export only firms are much more likely to do both (.44 probability) than investment only firms

(only .06 probability).

The transition patterns reported in Table 4 illustrate the need to model the investment and

exporting decision jointly. In our model, firms cannot export below a certain productivity cut-

off. Therefore firms need to invest and increase their productivity in order to export. The return

to investment can be higher or lower for exporting versus non-exporting firms, which makes the

probability that the firm will choose to invest dependent on the firm’s export status. Table 5

illustrates the average productivity constructed from equation 30 in each year for operating firms,

new entrants, firms that exit, and firms that operated in all 5 years.

5. Results

5.1. Demand, Cost and Productivity Evolution

The parameter estimates from the first stage estimation of equations 31 and 32 are reported in

Table 6. The first column reports the estimates using investment in capital, which we also use in

the dynamic model. The second column reports estimates using investment in R&D.

Focusing on the first column, the implied value of the demand elasticity for domestic and

export markets are 7.55 and 2.11. These elasticity estimates imply markups of price over marginal

cost of 15.3 percent for domestic market sales and 89.7 percent for foreign sales. The coefficient

on α1 measures the effect of the lagged productivity on current productivity and it is positive and

significant. The coefficient α4 measures the effect of investment on capital on current productivity.

Firms that increase their investment by 1% can increase their productivity by .03%. The effect of

past exporting on current productivity is given by α5. This a measure of learning-by-exporting’s

impact on productivity and in this case is not significant suggesting very little learning-exporting.

− 28 −


The last coefficient α6 measures the impact of product restructuring on productivity. Producing

one more product increases firm’s productivity by 6%. This suggests learning by diversifying.6

(more on this)?

Relative to a firm that never invests nor exports, a firm that invests an amount equal to the

average investment in capital goods and export will have mean productivity that is 111% higher. A

firm that does not export but able to invest the average investment is 104% higher in productivity.

A firm that only exports is 8% higher in productivity. A firm that produces one additional product

is 4.1% lower. While this provides a summary of the technology linkages between exporting,

investing, diversifying, and productivity, it does not recognize the impact of this process on the

firm’s choice to enter into operation and exporting. This behavioral response is the focus of the

second stage estimation. Given the estimates in Table 6 we construct estimate of firm productivity

from equation 30. The mean of the productivity estimates is 2.36 among operating firms and

the (.05, .95) percentiles of the distribution are (1.97, 2.78). The mean of productivity estimates

including the 0’s is 1.47 with (.05, .95) percentiles of the distribution (0, 2.7). The variation in

productivity will be important in explaining which firms self-select into entry/exit, exporting and

diversifying.

We can assess how well the productivity measure correlates with the firm’s entry/exit, export

and product restructuring choices. In the top panel of Table 7 we report estimates of a probit

regression of exporting on the firm’s productivity, lagged investment on capital goods, lagged

export dummy, lagged number of products, and a set of time, industry, and time cross industry

dummies. This regression is similar to the reduced form policy functions that come from our

dynamic model. The export demand shocks are not included explicitly but rather captured in the

error terms. In the probit model, all the coefficients are highly significant. Both productivity and

lagged export status play a positive and significant role in determining the current export status.

The coefficients on investment and product restructuring are negative and significant, suggesting

crowding out effect from investment and product restructuring. In the second and third row of the

top panel we report OLS regressions of export revenue for firms in the export market in equation

(). The explanatory variables are productivity and a set of dummies (industry, time, and industry

6The second column repeats the estimation using log of R&D expenditure rather than log of investment on capitalgoods. This does not change any sign nor significance of the coefficients in the model.

− 29 −


cross time effects). The lagged export dummy and investment choice do not affect the volume once

the firm is in the export market. Since the Spanish firm data does not provide information on how

many products firms export, the number of products choice is also not included. The R square

term for the regression without fixed effects is .66 and .69 for the regression without fixed effects,

suggesting export demand heterogeneity is not a source of size and profit differences in the export

market. (more on this)

The first row of the second panel in Table 7 reports estimates of a probit regression of firm

exit. Firm is defined as exit in period t if it has zero total revenue (domestic plus export) in the

period t+1. This definition of firm exit is consistent with the way we model firm entry/exit where

we assumed in each period firms make their production decisions, produce, and decide if they want

to exit and receive a scrap value at the end of the period. Firms with higher productivity are less

likely to exit the market. This is both economically and statistically significant. The parameter on

investment is insignificant. Multi-product firms are less likely to exit the market. Being an exporter

in the past makes the firm more likely to exit. One explanation for this is firms involved in the

export market are more likely to respond to the negative demand shocks in the export market.

(more on this, maybe do an exit to export market from existing exporting firms).

The last panel in Table 6 reports estimates of an OLS regression of firm’s product restructuring

choice.7 The dependent variable is the number of products firm chooses to produce. Firms with

higher productivity will produce more products.(more on this)

Overall, it is clear from these reduced form regressions that the productivity variable we have

constructed is measuring an important plant characteristic that is correlated with export and

entry/exit decisions and the firm’s export and domestic revenue once they choose to participate in

the market. We report the estimates of the dynamic investment equations in the next section.

5.2. Dynamic Estimates

The remaining cost, export demand parameters, entry and exit rates are estimated in the second

stage of the empirical model using the likelihood function that is the product over the firm-specific

joint probability of the data given in equation (). The coefficients reported in Table 8 are the means

and standard deviations of the parameters for the fixed and sunk cost of operation. The estimated

7Maybe do a multi-variate probit/logit or negative binomial regression later. but for now, OLS

− 30 −


fixed cost parameter is less than the sunk cost parameter, indicating that the firm entry cost is

substantially larger than the per-period costs of maintaining operation.

5.3. In-sample Model Performance

To assess the overall fit of the model, we use the estimated parameters to simulate patterns of firm

entry and survival, investment, exporting and product restructuring decision, transition patterns

between the choices, and productivity trajectories for the firms in the sample and compare the sim-

ulated patterns with the actual data. Since each firm’s productivity evolves according to equation

(), we need to simulate each firm’s trajectory of productivity jointly with its dynamic decisions. In

Table 9 we report the actual and predicted percentage of entry, exit, investment, export, product

restructuring and the mean productivity. Overall, the simulations do a good job of replicating these

average data patterns for all three variables.

6. Counterfactuals

6.1. Within Firm Effect

In our model, the determinants of a firm’s entry, exit, export, investment and product restructuring

choices are its current productivity and cost draws. We will isolate the role of current productivity

and the cost shocks on these activities. We do this by calculating the marginal benefit to each

activity. Table 12 reports the partial equilibrium marginal benefits of exporting with different

combinations of productivity and investment with entry and exit rate for calculated for firms optimal

strategies. The first column in the top panel reports the logged values of V (ϕ,X, I,N) with the

optimal investment, export, product restructuring, entry and exit strategy for each productivity

level. The second column reports the logged values of V (ϕ,X, I = 0, N), forcing investment to

be zero, allowing optimal export andproduct restructuring strategies every period, but take entry

and exit rate as given when we calculated for V (ϕ,X, I,N) . The third column reports the logged

values of V (ϕ,X = 0, I,N), forcing profit to be consistent of domestic revenue only and the optimal

investment and product restructuring strategy are recalculated based on domestic profit only. The

fourth column reports the logged value of V (ϕ,X = 0, I = 0, N) forcing both export and investment

to be zero. All the values in the four columns are increasing, reflecting the increase in profits with

− 31 −


higher productivity.

The fifth column reports the marginal benefit of exporting for a firm that is allowed to invest

in its future productivity and choose number of products to produce with entry and exit rate as

given. It is positive, reflecting the fact that a firm that does both activities has a higher future

productivity trajectory, and is increasing in current productivity implying that a high productivity

producer is more likely to self select into the export market. The benefit of exporting for a firm

that is not allowed to invest in its future productivity is reported in the sixth column and it is

also positive and increasing in the level of current productivity. Comparing the fifth and sixth

column, we see that the difference between the marginal benefits of exporting with investment and

without investment is positive, implying that the investment decision has important impact on the

return to exporting. This is what we call the market size effect or complementarity in export and

investment. The return to exporting is greatest for middle productivity firms because both low and

high productivity firms investment rate (investment/profit) are less than the middle productivity

investment rate.

Table 13 looks at the marginal benefit of exporting with different combinations of productivity

and product restructuring strategy with entry and exit as given. The third column reports the

logged values of V (ϕ,X, I,N = 1), forcing all firms to produce only one product with optimal

investment and export strategy but taking entry and exit as given before. The fourth column

reports the logged values of V (ϕ,X = 0, I,N = 1), not allowing firms to export nor to produce

more than one product. Again, all the values in the first four columns are increasing reflecting

higher profits with higher productivity. The fifth column is still the marginal benefit of exporting

for firms with optimal strategies in investment and product restructuring. The sixth column is

the marginal benefit of exporting for firms that are only allowed to produce one product. This

is positive and increasing in productivity. The last column in the second panel is the difference

between the marginal benefits of exporting for multi-product firms and firms that are allowed to

produce only one product. This number is positive for middle productivity firms and negative for

high productivity firms. Firms with higher productivity and higher profits, when opening up to

trade, tend to reduce the number of products produced to better focus on their core competency

groups to grab bigger market shares through exporting.

Table 14 looks at the marginal benefit of investment with different combinations of productivity

− 32 −


and product restructuring strategy with entry and exit as given. Column five reports the marginal

benefit of investment for firms with optimal product restructuring and export strategies. Column

six reports the marginal benefit of investment for firms that are not allowed to produce more than

one product. The last column reports the difference between the marginal benefits of investment

for multi-product firms and firms that produce only one product. We see the market size effect or

complementarity in investment and product restructuring present because the difference in marginal

benefit is positive for all productivity levels but is greatest for the middle productivity firms.

6.2. Between Firm Effect

We looked at the above counterfactuals with entry and exit rate as given in the previous section, in

this next section, we recompute entry and exit condition for each scenario and look at the general

equilibrium marginal benefits of these activities.

7. Conclusion

This paper estimates a dynamic structural model that captures the relationship between investment,

exporting and productivity for multi-product firms in the presence of endogenous entry and exit.

It characterizes a firm’s joint dynamic decision process for entry, exit, investment, exporting and

number of products as depending on its productivity, and fixed and sunk costs. It also describes

how a firm’s decisions on investment, exporting and product restructuring endogenously affect its

future productivity.

There are five broad conclusions we draw about the sources of productivity evolution among

Spanish firms. First, firm productivity evolves endogenously in response to the firm’s choice to

invest and diversify, but not to the choice to export. An one percent increase in investment raises

future productivity by three percent, and increasing the number of products produced by one raises

future productivity by 6 percent. Second, the marginal benefits of exporting vs. non-exporting in-

crease with firm’s productivity. The marginal benefits of investment versus zero investment is

positive; however it is greater for the middle productivity firms than for both low and high pro-

ductivity firms. The marginal benefits of multi-product versus single product reveals a similar

pattern. This leads to the self-selection of high productivity firms into exporting, investment, and

− 33 −


multi-products. When combined with the fact that decisions to diversify and invest lead to endoge-

nous productivity improvements, this further reinforces the importance of self-selection based on

current productivity as the major factor driving the decision to export, invest and produce multiple

products. Third, the cross-partials between exporting and investment, and investment and prod-

uct restructuring are positive for all firms. This suggests that both exporting and investment and

investment and product restructuring augment each other and further reinforce the self-selection

through the complementarity effect. However, the cross partial between exporting and product

restructuring is positive only for low and middle productivity firms and is negative for high produc-

tivity firms. This suggests that when opening up to trade, high productivity firms should decrease

the number of products produced in order to focus on their core competency products and grab a

greater market share through exporting. Fourth, the fixed cost of investment is smaller than the

fixed costs of exporting, which results in a larger proportion of firms choosing to invest than to ex-

port. The larger proportion of firms choosing to invest is also a result of investment having a larger

direct effect on future productivity. Finally, our counterfactual exercises show that a reduction in

trade costs will have a significant positive effect on both the probability and the amount that a

firm exports and invests, while the number of products produced is reduced. These three effects

lead to an overall increase in mean productivity. The combination of larger export markets, and

the firm’s ability to invest and change the number of products they produce to take the advantage

of larger export markets contributes to larger productivity gains.

Overall, our empirical findings emphasize the important role of heterogeneity in productivity

as the driving force in determining a firm’s total revenue and decision to export, invest and produce

multiple products. This is further reinforced by the fact that investment and product restructuring

decisions result in future productivity gains. The model can be extended in several ways. We

can include the distinction between different types of investment and determine the return to each

type of investment. The Spanish firm data includes investment expenditures on R&D, information

computing technologies, industrial machinery, land, building and furniture. We will be able to

look at whether one of the investment tools had a more substantial impact on the productivity. In

addition, we assumed perfect capital markets in this paper. We may explore the role of imperfect

capital market on the return to investment and therefore productivity for different sectors. Firms

in some sectors need to finance a greater share of their costs externally and sectors differ in their

− 34 −


endowment of tangible assets that can serve as collateral.

− 35 −


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Appendix

Sample Coverage and Data Collection

The ESEE’s population of reference is made up by the firms with 10 or more employees and whichbelong to what is usually known as the manufacturing industry. The geographical scope of referenceis all the Spanish territory, and the variables have a yearly temporal dimension.

One of the most relevant characteristics of the ESEE is its representativeness. The initialselection was carried out combining exhaustiveness and random sampling criteria. In the firstcategory were included those firms which have over 200 employees, and whose participation wasrequired. The second category was composed by the firms which employ between 10 and 200workers, which were selected through a stratified, proportional, restricted and systematic sampling,with a random start. In the first year, 1990, 2,188 firms were interviewed along the above mentionedcriteria. Later special care has been paid to maintaining its representativeness with regard to thepopulation of reference. The effort has been oriented, on the one hand, to reducing as far as possible,the deterioration of the initial sample, trying to avoid the reduction of the firms’ collaboration, andon the other, including each year into the sample all the newly incorporated firms which employover 200 workers, as well as a randomly selected sample which represents around 5

Computation of the Firm’s Dynamic Problem

− 39 −


Number of Firms

Median Domestic Revenue

Median Employment

Median Number of Products

2002 610 14.34 23 12003 495 15.96 24 12004 491 16.07 24 12005 716 17.46 22 12006 777 16.55 22 1

Average Domestic Revenue

Average Employment

Average Number of Products

2002 610 89.31 55.77 1.072003 495 110.20 63.09 1.092004 491 122.17 65.07 1.092005 716 137.17 67.57 1.092006 777 144.28 66.27 1.14

Number of firms

Median Domestic Revenue

Median Employment

Median Number of Products

Median Export

Revenue2002 1097 118.10 169 1 47.552003 885 127.06 175 1 52.282004 883 129.60 175 1 55.822005 1195 120.76 156 1 40.042006 1246 105.59 124 1 34.24

Average Domestic Revenue

Average Employment

AverageNumber of Products

Average Export

Revenue2002 1097 618.33 383.5 1.13 400.352003 885 671.04 400.3 1.14 455.222004 883 729.08 400.8 1.14 481.882005 1195 635.56 354.4 1.13 430.032006 1246 631.61 331.5 1.15 452.00

Exporters

Table 1Domestic and Export Revenue (in 100,000 Euros) and Firm Size

Non-exporters

This table provides summary statistics for firm sizes measured in revenues (in 100,000 Euros),average employment and for number of products produced for exporters and non-exporters. Thetop panel consists of median and average measures for non-exporters and the bottom panel consistsof median and average measures for exporters.

− 40 −


Year% of Nonzero

Investment

Median Positive

Investment

Average Positive

Investment

% of Nonzero

R&D

Median Positive

R&D Expenses

Average Positive

R&D Expenses

2002 69% 4.13 56.98 11% 4.18 22.392003 68% 5.37 53.55 9% 5.03 18.402004 71% 5.57 68.91 10% 4.68 28.592005 72% 5.31 65.66 11% 3.65 24.372006 67% 5.76 43.01 10% 6.00 10.47

Year% of Nonzero

Investment

Median Positive

Investment

Average Positive

Investment

% of Nonzero

R&D

Median Positive

R&D Expenses

Average Positive

R&D Expenses

2002 88% 57.54 391.25 51% 31.68 226.252003 86% 70.00 428.25 51% 36.90 316.132004 89% 61.75 393.10 52% 35.03 353.362005 90% 56.66 419.94 53% 34.14 314.862006 89% 48.46 416.41 50% 33.70 356.09

N of firms N of firms

610 1097

495 885

491 883

716 1195

777 1246

3,910,000

Non-exporters

Exporters

Table 2Investment and R&D Expenses (in 10,000 Euros)

This table provides summary statistics for firm investment and R&D expenditures (in 10,000 Eu-ros) for exporters and non-exporters. The top panel consists of median, and average investmentand R&D expenditures for non-exporters and the bottom panel consists of median and averageinvestment and R&D expenditures for exporters.

YearN of firms w/ positive Revenue

N of non-operating

firms

N of New Entrants

N of Exits Entry Rate Exit Rate

2002 1707 941 327 0.192003 1380 1268 0 6 0.00 0.002004 1374 1274 0 97 0.00 0.072005 1911 737 634 195 0.33 0.102006 2023 625 307 0.15

Average 1679 969 235.25 156.25 0.14 0.09

625

Table 3Entry and Exit

This table provides number of entry and exit and operating firms in each year.

− 41 −


Status Year t Neitheronly

Investmentonly

ExportBoth

All Incumbents 0.11 0.25 0.07 0.57

Neither 0.67 0.29 0.01 0.02only Investment 0.14 0.79 0.01 0.06only Export 0.04 0.03 0.49 0.44Both 0.00 0.02 0.06 0.92

All New Entrants 0.16 0.32 0.08 0.43Neither 0.49 0.40 0.03 0.08only Investment 0.20 0.72 0.00 0.08only Export 0.03 0.00 0.45 0.52Both 0.00 0.03 0.06 0.91

All Exiting Firms 0.27 0.17 0.11 0.45Neither 0.88 0.10 0.02 0.00only Investment 0.44 0.54 0.00 0.02only Export 0.03 0.00 0.42 0.55Both 0.00 0.01 0.04 0.95

Annual Transition Rates for New Entrants

Annual Transition Rates for Firms that Exit in t+2

Table 4Transition Rates for Incumbents, New Entrants, and Exiting Firms

Status Year t+1Annual Transition Rates for Incumbents

This table provides the average annual transition rates for incumbent firms, new entrants andexiting firms in four possible activities: only invest, only export, both, and neither.

Status Year t Neither Only Investment Only Export Both

All Firms 0.11 0.25 0.07 0.57

Neither 0.67 0.29 0.01 0.02

Only Investment 0.14 0.79 0.01 0.06

Only Export 0.04 0.03 0.49 0.44

Both 0.00 0.02 0.06 0.92

Annual Transition Rates for Operating Firms

Status Year t+1

This table provides the average log productivity for new entrants, exiting firms, and incumbentfirms in each year. The productivity measure is constructed using Levinsohn and Petrin (2003)approach.

− 42 −


Parameter Coef St. Error

ρd 0.87 * ( 0.01)

ρx 0.53 * (0.01)

R‐Square 0.99

sample size 4740

Capital R&D

intercept 0.04 (0.13) 0.50 (0.29)

productivity (t‐1) 0.72 * (0.15) 0.30 (0.41)

productivity (t‐1)2 0.03 (0.10) 0.33 (0.20)

productivity (t‐1)3 ‐0.01 (0.02) ‐0.05 (0.03)

investment (Ii,t‐1) 0.03 * ( 0.01) 0.03 * (0.01)

export (Xi,t‐1) 0.00 ( 0.02) 0.03 (0.05)

product restr. (Ni,t‐1) 0.06 * ( 0.01) 0.06 * ( 0.01)

R‐Square 0.98 0.97

sample size 4740 2121

Table 1

Variable Cost

Table 2

Productivity Evolution

Investment measured as:

This table provides the estimated coefficients for equation () and (). The top panel provides theestimates for elasticity of substitution for domestic and export market, respectively. The bottompanel provides the estimates for the productivity evolution. *** indicates significance at 1%. ** at5%, * at 10%.

− 43 −


Parameter Mean St. Dev. ThousandsEntry sunk cost 19.7 2.25 € 359,000Domestic fixed cost 12 0.41 € 160Product fixed cost 11 0.36 € 59Export fixed cost 13.5 0.45 € 730Investment Fixed Cost 10.4 0.32 € 32d (investment cost) 1 0.01Avg sell-off value 16 0.92 € 8,900

Table 3Dynamic Parameter Estimates

This table provides the estimated coefficients for equation () and () in reduced form. The toppanel provides the estimates for export decision in a probit model using productivity measuresconstructed from before. The middel panel provides the estimates for exit decision in a probitmodel. The last panel provides estimates from an OLS regression of number of products on firmproductivities. *** indicates significance at 1%. ** at 5%, * at 10%.

Parameter Mean St. Dev. In EurosEntry sunk cost 19.7 2.25 359 millionDomestic fixed cost 12 0.41 .16 millionProduct fixed cost 11 0.36 59 thousandExport fixed cost 13.5 0.45 .73 millionInvestment Fixed Cost 10.4 0.32 32 thousandd (investment cost) 1 0.01avg sell-off value 16 0.92 8.9 million

Table 8Dynamic Parameter Estimates

This table provides the estimated coefficients for the dynamic parameters in the model and thecorreponding dollar values for these estimates.

− 44 −


export participation Average Productivityactual 0.63 Actual 2.22predicted 0.62 Predicted 2.36

Investment Exit rateActual 15.41 Actual 0.09Predicted 15.75 Predicted 0.06

Entry rateActual 0.15Predicted 0.07

Table 9In-Sample Performance

This table shows the in-sample performance for estimated static and dynamic parameters.

− 45 −


This graphs shows that investment, export and productivity are all correlated.

− 46 −


This graphs shows how the investment, export, and profits change when a country is opening upto trade. The top panel shows the change in profits when a country is opening up to trade. Thebottom panel shows the change in investment profile when a country is opening up to trade. ϕit isthe productivity. ϕA

∗i is the productivity cut-off in autarky below which firms cannot operate. ϕCT

∗i

is the productivity cut-ff when a country goes from autarky to trading, below which firms cannotoperate. ϕCT

∗ix is the productivity cut-off for exprting firms, below which firms cannot export.

− 47 −


productivity V(X,I,N) V(X,I=0,N) V(X=0,I,N) V(X=0,I=0,N) MBEMBE (I=0)

MBE -MBE(I=0)

1.9 16.44 16.44 16.44 16.44 0.00 0.00 0.002 16.73 16.48 16.66 16.48 0.08 0.00 0.08

2.1 16.96 16.53 16.80 16.53 0.16 0.00 0.162.2 17.27 16.57 16.98 16.57 0.29 0.00 0.292.3 17.65 16.66 17.21 16.66 0.43 0.00 0.432.4 18.08 16.84 17.49 16.80 0.59 0.04 0.552.5 18.53 17.14 17.79 17.02 0.74 0.11 0.622.6 18.98 17.55 18.11 17.32 0.87 0.23 0.642.7 19.43 18.13 18.49 17.76 0.94 0.37 0.572.8 19.77 18.81 19.00 18.29 0.77 0.51 0.262.9 20.40 19.53 19.57 18.87 0.84 0.66 0.183 21.10 20.30 20.16 19.50 0.94 0.80 0.14

Table 12 Investment and Export Complementarity

This table shows the investment and export complementarity. All values are in logs. MBE ismarginal benefit of exporting and is defined as V(X,I,N)-V(X=0,I,N), where V(X,I,N) is the valuefunction when all three choices, X, I, and N are chosen optimally and the dynamic parameters arecomputed using maximum likelihood estimator. V(X=0,I,N) is the value function when export isrestricted to 0 and I and N are chosen optimally with entry and exit rate fixed as in V(X,I,N).MBE (I=0) is the marginal benefit of exporting when investment is restricted to 0 and is defined asV(X,I=0,N)- V(X=0, I=0, N). The cross partial between I and X is defined as MBE - MBE (I=0).

− 48 −


Investment Complementarity

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3log productivity

log

V

MBE MBE(I=0)

I complementarity

This graph shows the investment and export complementarity. The thin continuous line plots theMBE defined before, the dotted line plots the MBE (I=0), and the dashed line plots the crosspartial between investment and export, or what we call investment complimentarity.

− 49 −


productivity V(X,I,N) V(X=0,I,N) V(X,I,N=1) V(X=0,I,N=1) MBEMBE (N=0)

MBE-MBE(N=0)

1.9 16.44 16.44 16.44 16.44 0.00 0.00 0.002 16.73 16.66 16.67 16.63 0.08 0.04 0.04

2.1 16.96 16.80 16.83 16.73 0.16 0.09 0.072.2 17.27 16.98 17.04 16.86 0.29 0.18 0.112.3 17.65 17.21 17.32 17.01 0.43 0.30 0.132.4 18.08 17.49 17.67 17.19 0.59 0.48 0.112.5 18.53 17.79 18.06 17.39 0.74 0.66 0.072.6 18.98 18.11 18.47 17.75 0.87 0.71 0.162.7 19.43 18.49 18.86 18.20 0.94 0.66 0.282.8 19.77 19.00 19.49 18.72 0.77 0.77 0.002.9 20.40 19.57 20.18 19.27 0.84 0.91 -0.073 21.10 20.16 20.93 19.82 0.94 1.11 -0.17

Table 13 Multiproduct and Export Complementarity

This table shows the multi-product and export complementarity. All values are in logs. MBE ismarginal benefit of exporting and is defined as V(X,I,N)-V(X=0,I,N), where V(X,I,N) is the valuefunction when all three choices, X, I, and N are chosen optimally and the dynamic parameters arecomputed using maximum likelihood estimator. V(X=0,I,N) is the value function when export isrestricted to 0 and I and N are chosen optimally with entry and exit rate fixed as in V(X,I,N).MBE (N=0) is the marginal benefit of exporting when number of products is restricted to 1 and isdefined as V(X,I,N=1)-V(X=0, I, N=1). The cross partial between N and X is defined as MBE -MBE (N=1).

− 50 −


Multiproduct Complementarity

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3

log productivity

log

V

MBE MBE(N=1) Multiproduct complementarity

This graph shows the multi-product and export complementarity. The thin continuous line plotsthe MBE defined before, the dotted line plots the MBE (N=1), and the dashed line plots the crosspartial between multi-product and export, or what we call multi-product complimentarity.

− 51 −


productivity V(X,I,N) V(X,I=0,N) V(X,I,N=1) V(X,I=0,N=1) MBIMBI

(N=1)MBI -

MBI(N=1)

1.9 16.44 16.44 16.44 16.44 0.00 0.00 0.002.0 16.73 16.48 16.67 16.48 0.25 0.19 0.062.1 16.96 16.53 16.83 16.52 0.43 0.30 0.132.2 17.27 16.57 17.04 16.56 0.70 0.48 0.222.3 17.65 16.66 17.32 16.64 0.99 0.67 0.312.4 18.08 16.84 17.67 16.81 1.24 0.86 0.382.5 18.53 17.14 18.06 17.07 1.39 0.99 0.402.6 18.98 17.55 18.47 17.48 1.43 0.99 0.442.7 19.43 18.13 18.86 18.04 1.30 0.82 0.482.8 19.77 18.81 19.49 18.71 0.97 0.78 0.192.9 20.40 19.53 20.18 19.44 0.87 0.74 0.133.0 21.10 20.30 20.93 20.22 0.80 0.72 0.08

Table 14 Investment and Multiproduct Complementarity

This table shows the investment and multi-product complementarity. All values are in logs. MBI ismarginal benefit of investment and is defined as V(X,I,N)-V(X,I=0,N), where V(X,I,N) is the valuefunction when all three choices, X, I, and N are chosen optimally and the dynamic parameters arecomputed using maximum likelihood estimator. V(X,I=0,N) is the value function when investmentis restricted to 0 and X and N are chosen optimally with entry and exit rate fixed as in V(X,I,N).MBI (N=1) is the marginal benefit of investment when number of products is restricted to 1 andis defined as V(X,I,N=1) - V(X, I=0, N=1). The cross partial between I and N is defined as MBI- MBI (N=1).

− 52 −


Multiproduct and I

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3log productivity

log

V

MBI MBI(N=1) Multiproduct complementarity

This graph shows the investment and multi-prodcut complementarity. The thin continuous lineplots the MBI defined before, the dotted line plots the MBI (N=1), and the dashed line plotsthe cross partial between investment and multi-product, or what we call investment-multi-productcomplimentarity.

− 53 −


Table

Su

mm

ary

of

the s

am

ple

’s e

volu

tion

in

th

e y

ears

19

90

-20

08

1

99

1

19

92

1

99

3

19

94

1

99

5

19

96

1

99

7

19

98

1

99

9

20

00

2

00

1

20

02

2

00

3

20

04

2

00

5

20

06

2

00

7

20

08

1. C

urr

en

t sa

mp

le

2188

2059

1977

1869

1876

1703

*

1716

1920

1776

1754

1870

1724

1708

1380

1374

1911

2023

2013

1

.1 F

irm

s w

hic

h

an

swer

1888

1898

1768

1721

1693

1584

1596

1764

1631

1634

1693

1635

1380

1374

1277

1716

1892

1853

1

.2 D

isap

pear1

62

52

72

53

51

28

35

18

45

38

20

18

51

4

17

35

30

57

1

.3 D

o n

ot

collab

ora

te

187

62

124

45

55

33

54

22

35

24

0

12

88

0

12

14

18

10

1

.4 N

o a

ccess

2

51

47

13

50

77

58

31

116

65

58

157

59

189

2

68

146

83

93

2. R

eco

vere

d3

129

99

73

46

0

3

2

3. En

trie

s in

th

e c

urr

en

t year

42

79

101

56

9

132

324

12

123

236

31

0

0

0

588

307

118

154

Nu

mb

er

of

reco

rd o

n f

ile

2359

2438

2539

2595

2604

2736

3060

3072

3195

3431

3462

3462

3462

3462

4050

4357

4475

4629

Not

as:

1.

Clo

sure

s, f

irm

s in

liq

uid

ation,

chan

ge

to a

non-m

anufa

cturing a

ctiv

ity,

dis

appea

rance

thro

ugh m

erger

or

acquis

itio

n.

2.

Can

not

be

found,

pro

visi

onal

clo

se-u

p.

3.

In 1

991 t

hey

are

lar

ge-

size

d f

irm

s to

whic

h t

he

ques

tion

nai

re w

as a

lrea

dy

subm

itte

d in 1

990,

but

whic

h d

id n

ot a

nsw

er it.

In 1

994 it

is m

ade

up o

f la

rge-

size

d firm

s w

hic

h h

ad fill

ed t

he

ques

tion

nai

re b

efor

e but

whic

h a

t so

me

tim

e th

ey s

topped

doi

ng it.

*

Incl

udes

a c

om

pan

y w

hic

h d

id n

ot

colla

bora

ted in 1

995 b

ut

whic

h c

olla

bora

ted in 1

996.

The table shows the evolution of the sampled firms during the period 1990-2007− 54 −


1

SAMPLE COVERAGE ESEE 2005*

Less than

20 21 to 50 51 to 100 101 to 200 More than

200 Meat-processing industry 1.54% 3.03% 2.04% 14.29% 32.00%Foodstuffs and tobacco 2.42% 3.10% 3.97% 5.32% 38.75%Drinks 3.32% 3.40% 7.41% 23.81% 41.03%Textiles 3.06% 3.75% 6.98% 16.04% 42.62%Leather and footware 3.03% 4.67% 5.63% 14.81% 14.29%Wood industry 1.37% 3.25% 7.69% 16.67% 50.00%Paper 3.53% 3.38% 6.82% 14.29% 60.53%Editing and printing 1.98% 2.96% 6.67% 7.08% 40.32%Chemical industry 2.25% 4.28% 6.61% 11.03% 39.16%Rubber and plastics 3.09% 2.95% 5.79% 12.90% 46.43%Non-metallic minerals products 2.35% 3.34% 2.60% 10.18% 43.40%Iron and steel 2.12% 3.02% 5.65% 14.29% 48.57%Metallic products 2.01% 2.88% 5.31% 7.45% 41.67%Machinery and mechanical goods 2.41% 3.27% 5.42% 12.84% 51.95%Office machinery, computers, processing, optical and similar 1.54% 5.63% 13.64% 4.55% 45.45%Electrical and electronic machinery and material 3.06% 3.95% 4.81% 11.70% 45.83%Motor vehicles 2.74% 3.85% 6.19% 12.66% 44.85%Other transport material 1.57% 6.15% 13.04% 44.00% 31.58%Furniture 2.45% 3.31% 4.86% 12.00% 50.00%Other manufacturing 3.06% 2.73% 2.70% 9.38% 40.00%Total 2.36% 3.37% 5.44% 11.40% 42.95% * Sample coverage, calculated with respect to the Spanish Social Security Census

The table shows the sample coverage.

− 55 −

product restructuring, exports, investment, and growth...

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